Rodriguez is reportedly looking to leave the struggling rojiblancos after falling out of favour at the Vicente Calderon – and is believed to be keen to link up with fellow countryman Javier Mascherano on Merseyside.
The 29-year-old, who can also play as an attacking midfielder, has scored 10 goals in 35 appearances for Diego Maradona's side – including the stunning extra-time winner that knocked Mexico out of the 2006 World Cup.
Rodriguez is desperate to secure regular first-team football in order to ensure his place on the plane to this summer's global showpiece in South Africa.
However, both Liverpool boss Rafael Benitez and the player's agent Jose Segui have denied that a deal for the player is close to being sealed.
"It's true we've talked to Atletico Madrid and we're interested in the player but still it's just conversations," Benitez told Liverpool's official website.
"You never know with timescales. It's a question of everything being more or less agreed, and now it's for Atletico and the player to talk and see what happens."
While Segui told calciomercato.it: "We are working. It's true we have spoken [with Liverpool], but there is nothing definitive.
"I don't know when the negotiation could be closed. It's up to the two clubs and to their decision."
